What is the value of 0.1-tanh(0.1) ?

The value of 0.1-tanh(0.1) is 1/10-(e^{1/10}\sqrt[10]{e}-1)/(e^{1/10)\sqrt[10]{e}+1}

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0.1-tanh(0.1)

0.1 - tanh (0.1)

Decimal Notation

0.00033 \dots

Solution steps

0.1 - tanh (0.1)

= \frac{1}{10} - tanh (\frac{1}{10})

Rewrite using trig identities:

tanh (\frac{1}{10})

Use the Hyperbolic identity:

tanh (x) = \frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}}

= \frac{e ^{\frac{1}{10}} - e ^{- \frac{1}{10}}}{e ^{\frac{1}{10}} + e ^{- \frac{1}{10}}}

\frac{e ^{\frac{1}{10}} - e ^{- \frac{1}{10}}}{e ^{\frac{1}{10}} + e ^{- \frac{1}{10}}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

Join

Convert element to fraction:

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

Join

Convert element to fraction:

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

Divide fractions:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

Cancel the common factor:

sin (2 π \cdot \frac{1}{3})

\frac{1}{tan ( 2 5 ^{\circ} )}

cos (\frac{3 π}{33})

tan (16.2 6^{\circ})

\frac{500}{tan ( 1 5 ^{\circ} )}

What is the value of 0.1-tanh(0.1) ?
The value of 0.1-tanh(0.1) is 1/10-(e^{1/10}\sqrt[10]{e}-1)/(e^{1/10)\sqrt[10]{e}+1}